ABSTRACT
This study explores the inherent nonlinearity of quarter car models by employing an experimental and numerical approach. The dynamics of vehicular suspension systems are pivotal for ensuring passenger comfort, vehicle stability, and overall ride quality. In this paper we assessed the impact of various parameters and components on suspension performance, enabled the optimization of ride comfort, stability, and handling characteristics. Firstly, experimental analysis allowed for the investigation of factors that are challenging to model theoretically, such as stiffness nonlinearity and damping characteristics, which may vary under different operating conditions. Time domain and frequency response diagram of the model has been obtained. Secondly, a quarter-car with single degree-of-freedom presented and investigated in fractional order form. Fractional order dynamics emphasize nonlinearities in quarter car models, capturing real-world dynamics effectively. The proposed fractional-order nonlinear quarter car model employed Caputo derivative. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used and the disturbance of road assumed to be stochastic. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude and frequency on vehicle vibration is investigated.
ABSTRACT
The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme stems from its known importance in fractional calculus, an area of study that has attracted significant interest in the mathematical sciences and physics. Because of its special capacity to accurately represent physical memory and inheritance, the Caputo derivative is a relevant and appropriate option for representing the fractional features present in the issues this study attempts to address. Moreover, a detailed Fourier analysis of the explicit finite difference scheme's stability is shown, demonstrating its conditional stability. Finally, certain numerical example solutions are reviewed and MATLAB-based graphic presentations are made.
ABSTRACT
The infection of human papilloma virus (HPV) poses a global public health challenge, particularly in regions with limited access to health care and preventive measures, contributing to health disparities and increased disease burden. In this research work, we present a new model to explore the transmission dynamics of HPV infection, incorporating the impact of vaccination through the Atangana-Baleanu derivative. We establish the positivity and uniqueness of the solution for the proposed model HPV infection. The threshold parameter is determined through the next-generation matrix method, symbolized by [Formula: see text]. Moreover, we investigate the local asymptotic stability of the infection-free steady-state of the system. The existence of the solutions of the recommended model is determined through fixed-point theory. A numerical scheme is presented to visualize the dynamical behavior of the system with variation of input factors. We have shown the impact of input parameters on the dynamics of the system through numerical simulations. The findings of our investigation delineated the principal parameters exerting significant influence for the control and prevention of HPV infection.
Subject(s)
Papillomavirus Infections , Public Health , Humans , Sexual Behavior , Human Papillomavirus Viruses , Cost of IllnessABSTRACT
In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam-Hyers-Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results.
